25 + X^2 - 10*x*y = 16, 64 + x^2 -16*x*y = (32/5)^2

asked by guest
on Jan 31, 2025 at 12:27 am



You asked:

Solve the system of equations:25+X210xy=1664+x216xy=(325)2\begin{aligned}25 + {X}^{2} - 10 x y &= 16\\64 + {x}^{2} - 16 x y &= {\left( \frac{32}{5} \right)}^{2}\end{aligned}

MathBot Answer:

The system of equations has infinitely many solutions.

X=80y216y25y299x=8y8(5y3)(5y+3)5\begin{aligned}X &= \sqrt{80 y^{2} - 16 y \sqrt{25 y^{2} - 9} - 9}\\x &= 8 y - \frac{8 \sqrt{\left(5 y - 3\right) \left(5 y + 3\right)}}{5}\end{aligned}

yy is a free variable.